However, these are not strictly Penrose tilings. To make a quilt that has that quirky stars-with-ripples effect that the aperiodic tiling creates, you need to follow the matching rules:

My first plan was to design a quilt that copied the curved design as shown in the above diagram (but just the pink lines):

NOTE: Penrose tiling is beyond the powers of Electric Quilt, so I designed these using Geometer's Sketchpad instead.

I made this pot holder as a test to see if it was feasible to make the entire full sized quilt this way:

Although this was strictly feasible, I found that all the curved lines and sharp points made this too tricky for my skill level.

So I decided to tweak the matching rules into straight lines:

This way I can machine piece these straight lines first and paper piece the rhombi.

Constructing Penrose Tiling using Inflation/Deflation Properties

One of the mind-bending properties of a Penrose tiling is that if all the rhombi in a given tiling are broken up like so:

The resulting tiling is also a Penrose tiling of smaller tiles. In this example I deflate this simple tiling one level:

Now I can deflate this tiling down another level (I shaded a couple of rhombi from the previous level to illustrate this):

You can continue this indefinitely. Here's 3 and 4 level deflation:

The flip side of this is inflation; any tiling can be combined into larger tiles by reversing this process. So any tiling, no matter how large, is only a subset of a single rhombus (mind = blown).

This inspired me to design a quilt that exploits this property. I first thought it would be interesting to have a quilt that uses different sized rhombi:

Then I thought it would be cool if I designed a quilt where all the rhombi were the same size, but by using different colors and/or values (light and dark), an inflated level of Penrose tiling would emerge:

The combination of this design with the matching rule design above became the final design for the Christmas tree skirt: